A line of best fit does not go through your measured points but between them, with about as many points above as below. That is how you average out your uncertainties, and that is why you then read off the line and not off a single point.
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I measure the same thing six times: same table, same ruler, same stack of books. I put my six points in a graph, and no straight line goes exactly through all six. That feels like bad measuring. It is exactly right.
In this video you learn how to make a graph from a series of measurements and read something out of it again. You see the fixed form of a table and of a graph: quantity with its unit, what you set yourself horizontally, a scale in steps of one, two or five, and a break in the axis if you do not start at zero. Then comes the part where almost everyone does it differently from how it should be: you do not join your points to each other, you lay one smooth line between them. That line of best fit has about as many points above it as below, and with that you average out your uncertainties.
And then the reading off. From that moment you read off the line and not off your own point, because the line is the average of all your measurements and the point is only one of them. Reading a value between your measurements is called interpolating. Extending your line beyond your measurements is called extrapolating, and that is something else: there you assume the relationship simply continues, and you are supposed to say that you are assuming it.
For upper secondary physics, in the basic skills.
In this video
The full explanation, in writing
No line fits through all six
0:00I measure the same thing six times. Same table, same ruler, same stack. I put my six points in a graph. And no straight line goes exactly through all six.
The fixed form of a table
0:15Before you draw anything, you put your measurements in a table. That table has a fixed form, and that is not tidiness but readability. Above each column the quantity, with the unit behind it in brackets. One row per measurement. And on the left you put the quantity you set yourself.
0:33For me that is the number of books on the table: zero, two, four, six, eight, ten. On the right stands what I measure, the height of the top book above the floor.
The fixed form of a graph
0:45From that table you make a graph. That too has a fixed form. The axes are at right angles to each other. The quantity you set goes horizontally, and if time is one of the two, then time always goes horizontally. What you measure goes vertically.
1:02At each axis stands an arrow with the quantity, and the unit in brackets behind it. Your scale goes in steps of one, two or five, possibly times a power of ten, because you can read between those. Steps of three nobody can read. And you choose the scale so that your graph fills your whole diagram.
1:23Not from zero, you put a break in the axis: that is called an axis break, and it is there so nobody thinks that your graph starts at zero. You investigate how far a car rolls out at different starting speeds. Which of those two do you put horizontally?
The line of best fit goes between them
1:41Now the points. Each pair of numbers from your table becomes one point, and it stays visible, even when a line runs through it later. Then the part where almost everyone does it differently from how it should be. You do not join the points to each other.
1:57You draw a smooth line that shows the relationship as well as possible, and it may well run just past a few points. That line is called the line of best fit. Make sure about as many points lie above as below, then you average out your uncertainties.
2:15If you are sure it is a straight line, you draw a straight line. So not: every point is sacred. But: all the points together beat each point apart.
Reading off, interpolating and extrapolating
2:28What you read off from now on, you read off the line and not off your point. At six books I had measured ninety-three point four centimetres. On the line I read off ninety-three point one, and that is the better number. Take your point, you take one measurement instead of all six.
2:49I measured every two books, so at five books I have nothing. Still I can read it off: ninety point zero centimetres. Reading a value between your measurements is called interpolating. And I can also extend my line. At fourteen books I get about a hundred and nineteen centimetres.
3:12That is called extrapolating, and that is other than interpolating: beyond your measurements you assume the relationship simply continues. At fourteen books the stack might well start to wobble, and then none of it holds.
Three things to remember
3:29Three things. Table and graph have a fixed form: quantity with unit, what you set horizontally, and a scale in steps of one, two or five. The line does not go through your points but between them as well as possible, with as many points above as below.
3:48And you read off on the line. Between your measurements that is interpolating, beyond them extrapolating, and that last one is an assumption.
Two questions
3:58Two questions. One. You have eight points and you draw a straight line of best fit. Four points lie above it and four below, and no point lies exactly on it. Have you measured badly? Two. You measured between twenty and sixty degrees. Someone asks you what happens at a hundred and twenty degrees.
4:18What is your answer?
The answers
4:20The first: no, that is exactly right. Four above and four below means that you have averaged out your uncertainties. If every point lay exactly on the line, I would start doubting your measurements. The second: you do not know. You can extend your line and name a number, but that is extrapolating, and that is an assumption and not a measurement.
4:44Say that you are assuming it, or measure further.
Closing
4:49You can now graph a series of measurements, and lay a line through it that fits your measurements. Once you read from the shape of that line what the constant means, this is exactly what you need.
Frequently asked questions
Why may you not join your measured points to each other?
Because every point carries its own uncertainty. Joining them makes each measurement sacred, while the whole set together is better than any point apart. One smooth line between the points averages those uncertainties out.
What is the difference between interpolating and extrapolating?
Interpolating is reading a value between your measurements, and your line covers that. Extrapolating is extending the line beyond your measurements, and there you assume the relationship simply continues. That is an assumption, not a measurement, and you say so.
What is an axis break and when do you use it?
A break drawn in the axis, used when your scale does not start at zero. It is there so nobody reading your graph thinks it starts at zero, because that would make the relationship look different from what it is.
Which quantity goes horizontally in a graph?
The one you set yourself, and what you measure goes vertically. If time is one of the two, time always goes horizontally, whether you set it or not.
Why do you read off the line and not off your own measured point?
Because the line uses all your measurements and the point only one. At six books I had measured 93.4 centimetres and the line gives 93.1, and that is the better number, because the line has already averaged out the uncertainties.
After this comes which relationship you see in your graph, and which constant belongs with it.
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Physics with Thomas: physics explained with pictures where they add something, and without them where they distract.
In this series
Quantities and unitswhy 20,000 is not more than 10,0007:30
Ratios and percentagesone table for both3:15
Scientific notationpowers of ten and order of magnitude5:22
Calculating with powers of tenthe four rules3:18
Pythagoras and trigonometrywhich side with which angle3:19
Deriving units from a formulaconverting to base units7:47
Significant figureshow many figures do you write6:24
Line of best fitthe line touches no point5:07
Relationships and the constantbraking twice as fast5:20
Linearising a graphyour measurements never change4:41
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.